"Your mother has a restaurant."
Translation:Moren din har en restaurant.
I've taken few lessons with a private teacher, and one of the few things she taught me was that "Mora min" or "Dattera min" (the possessive after the family member) is a non elegant form. Instead, she suggested me to use a proper form such as "Min mor", "Min far", etc.
In all the exercise here only the first form is ever found, and I was wondering if I'm not learning the wrong forms
This is a good reason to get some outside reference and read some other materials. You'll get a much better idea exactly which forms are applicable where if you read them in gossip magazines/newspapers/letters to friends, etc.
It's fine to argue whether something is to formal or not, but it's difficult to get a sense of when to use something or avoid it with just someone telling you.